If you are really nervous, a trick I have heard of is to start with a really thick piece of beef. Then sear it on both sides in a hot pan. At this point the outside would be deemed safe and the interior is typically safe so you cut away the cooked parts. Then proceed to make the steak tartare with the still raw inside part. As a bonus those nice browned parts from the outside are a treat for the chef.

Use fresh beef that has been properly stored and handled. The natural state of beef is generally sterile, external pathogens are introduced in processing and multiply quickly on the beef. A good butcher who maintains a clean environment significantly decreases the chances of contamination. Keeping the beef cold until eaten slows the reproduction of any bacteria that happen to have made a home on your meat.

There is always a small risk of contamination, so people with compromised immune systems shouldn't eat raw meat. Most others are able to fight off bacterial infections, although it won't be pleasant.

I have eaten raw beef (including store bought ground beef) all my life. In fact, my mother told me our butcher fed me a small ball of raw, ground beef when I was a baby. She said it was my first solid food. I am now 80 years old & have never had any type of food borne illness, Probably have eaten at least a thousand pounds of raw beef of almost all cuts, gallons of raw oysters including some in southern Mexico, & still tell the waiter in the resturants "just knock off their horns, wipe their ----, & throw it on the plate" My step dad always said the way I ate a steak was "put a bandaid on it & it will get well", but he is now deceased, may he RIP.

I'm glad things have worked out for you, but it's definitely not always that way - entities like the FDA recommend cooking meat for a reason. The other answers here are a lot more realistic, telling people what they need to know to be confident they will be safe, even if they're not as lucky as you.
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Jefromi♦Jul 16 '12 at 16:52